Affine Multiple Yield Curve Models

Abstract

We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or HJM modeling, can be consolidated. We model a numéraire process and multiplicative spreads between Libor rates and simply compounded OIS rates as functions of an underlying affine process. Besides allowing for ordered spreads and an exact fit to the initially observed term structures, this general framework leads to tractable valuation formulas for caplets and swaptions and embeds all existing multi-curve affine models. The proposed approach also gives rise to new developments, such as a short rate type model driven by a Wishart process, for which we derive a closed-form pricing formula for caplets. The empirical performance of two specifications of our framework is illustrated by calibration to market data.

Keywords: Multiple yield curves, Libor rate, forward rate agreement, multiplicative spread, affine processes

JEL Classification: E43, G12